@Article{Mojdeh2016,
author="Mojdeh, Doost Ali
and Sayed-Khalkhali, A.
and Abdollahzadeh Ahangar, Hossein
and Zhao, Yancai",
title="Total $k$-distance domination critical graphs",
journal="Transactions on Combinatorics",
year="2016",
volume="5",
number="3",
pages="1-9",
abstract="A set $S$ of vertices in a graph $G=(V,E)$ is called a total‎ ‎$k$-distance dominating set if every vertex in $V$ is within‎ ‎distance $k$ of a vertex in $S$‎. ‎A graph $G$ is total $k$-distance‎ ‎domination-critical if $\gamma_{t}^{k} (G‎ - ‎x) < \gamma_{t}^{k}‎ ‎(G)$ for any vertex $x\in V(G)$‎. ‎In this paper‎, ‎we investigate some results on total $k$-distance domination-critical of graphs‎.",
issn="2251-8657",
doi="10.22108/toc.2016.11972",
url="http://toc.ui.ac.ir/article_11972.html"
}
@Article{Shiu2016,
author="Shiu, Wai Chee",
title="Extreme edge-friendly indices of complete bipartite graphs",
journal="Transactions on Combinatorics",
year="2016",
volume="5",
number="3",
pages="11-21",
abstract="Let $G=(V,E)$ be a simple graph‎. ‎An edge labeling $f:E\to \{0,1\}$ induces a vertex labeling $f^+:V\to Z_2$ defined by $f^+(v)\equiv \sum\limits_{uv\in E} f(uv)\pmod{2}$ for each $v \in V$‎, ‎where $Z_2=\{0,1\}$ is the additive group of order 2‎. ‎For $i\in\{0,1\}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎A labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|\le 1$‎. ‎$I_f(G)=v_f(1)-v_f(0)$ is called the edge-friendly index of $G$ under an edge-friendly labeling $f$‎. ‎Extreme values of edge-friendly index of complete bipartite graphs will be determined‎.",
issn="2251-8657",
doi="10.22108/toc.2016.12473",
url="http://toc.ui.ac.ir/article_12473.html"
}
@Article{Kadivar2016,
author="Kadivar, Mehdi",
title="A new $O(m+k n \log \overline{d})$ algorithm to find the $k$ shortest paths in acyclic digraphs",
journal="Transactions on Combinatorics",
year="2016",
volume="5",
number="3",
pages="23-31",
abstract="‎We give an algorithm‎, ‎called T$^{*}$‎, ‎for finding the k shortest simple paths connecting a certain‎ ‎pair of nodes‎, ‎$s$ and $t$‎, ‎in a acyclic digraph‎. ‎First the nodes of the graph are labeled according to the topological ordering‎. ‎Then for node $i$ an ordered list of simple $s-i$ paths is created‎. ‎The length of the list is at most $k$ and it is created by using tournament trees‎. ‎We prove the correctness of T$^{*}$ and show that its worst-case complexity is $O(m+k n \log \overline{d})$ in which n is the number of nodes and m is the number of arcs and $\overline{d}$ is the mean degree of the graph‎. ‎The algorithm has a space complexity of $O(kn)$ which entails an important improvement in space complexity‎. ‎An experimental evaluation of T$^{*}$ is presented which confirms the advantage of our algorithm compared to the‎ ‎most efficient $k$ shortest paths algorithms known so far‎.",
issn="2251-8657",
doi="10.22108/toc.2016.12602",
url="http://toc.ui.ac.ir/article_12602.html"
}
@Article{Hajisharifi2016,
author="Hajisharifi, Nasser
and Tehranian, Abolfazl",
title="A new construction for vertex decomposable graphs",
journal="Transactions on Combinatorics",
year="2016",
volume="5",
number="3",
pages="33-38",
abstract="Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S \subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x \in V(G)$. The graph $G\cup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $G\setminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G \cup W(S)$ is a vertex decomposable graph.",
issn="2251-8657",
doi="10.22108/toc.2016.13316",
url="http://toc.ui.ac.ir/article_13316.html"
}
@Article{Mao2016,
author="Mao, Yaoping
and Wang, Zhao
and Gutman, Ivan",
title="Steiner Wiener index of graph products",
journal="Transactions on Combinatorics",
year="2016",
volume="5",
number="3",
pages="39-50",
abstract="The Wiener index $W(G)$ of a connected graph $G$‎ ‎is defined as $W(G)=\sum_{u,v\in V(G)}d_G(u,v)$‎ ‎where $d_G(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$G$‎. ‎For $S\subseteq V(G)$‎, ‎the Steiner distance $d(S)$ of‎ ‎the vertices of $S$ is the minimum size of a connected subgraph of‎ ‎$G$ whose vertex set is $S$‎. ‎The $k$-th Steiner Wiener index‎ ‎$SW_k(G)$ of $G$ is defined as‎ ‎$SW_k(G)=\sum_{\overset{S\subseteq V(G)}{|S|=k}} d(S)$‎. ‎We establish‎ ‎expressions for the $k$-th Steiner Wiener index on the join‎, ‎corona‎, ‎cluster‎, ‎lexicographical product‎, ‎and Cartesian product of graphs‎.",
issn="2251-8657",
doi="10.22108/toc.2016.13499",
url="http://toc.ui.ac.ir/article_13499.html"
}